Effective Biomedical Experimentation Data by CICT Advanced Ontological Uncertainty Management Techniques

INTERNATIONAL JOURNAL OF BIOLOGY AND BIOMEDICAL ENGINEERING Volume 9, 2015

More effective biomedical experimentation data by CICT advanced ontological uncertainty management techniques

Rodolfo A. Fiorini

 from unique experiment. The remaining part is lost and Abstract—Classical experimental observation process, even in inevitably dispersed through environment into something we highly ideal operative controlled condition, like the one achieved in call "background noise" or "random noise" usually, in every current, most sophisticated and advanced experimental laboratories scientific experimental endeavor [2]. The amount of like CERN, can capture just a small fraction only of overall ideally information an individual can acquire in an instant or in a available information from unique experiment. A number of recent reports in the peer-reviewed literature have discussed lifetime is finite, and minuscule compared with what the milieu irreproducibility of results in biomedical research. Some of these presents; many questions are too complex to describe, let alone articles suggest that the inability of independent research laboratories solve, in a practicable length of time. to replicate published results has a negative impact on the A number of recent reports in the peer-reviewed literature development of, and confidence in, the biomedical research [3,4,5,6] have discussed irreproducibility of results in enterprise. Furthermore, poor reporting of health research is a serious biomedical research. Some of these articles suggest that the and widespread issue, distorting evidence, limiting its transfer into practice, and providing an unreliable basis for clinical decisions and inability of independent research laboratories to replicate further research. A series of papers published by the Lancet in published results has a negative impact on the development of, January 2014 highlighted the problems of waste in biomedical and confidence in, the biomedical research enterprise. research and the myriad of issues that can disrupt completion and use Furthermore, poor reporting of health research is a serious and of high quality research. To get more resilient data and to achive widespread issue, distorting evidence, limiting its transfer into higher result reproducibility, we present an adaptive and learning practice, and providing an unreliable basis for clinical system reference architecture for anticipatory smart sensing system interface. To design, analyse and test system properties, a simulation decisions and further research. A series of papers published by environment has been programmed in MATLAB language, called the Lancet [7] in January 2014 highlighted the problems of VEDA®. In this way, it is possible to verify and validate through waste in biomedical research and the myriad of issues that can numerical computation the behavior of all subsystems that compose disrupt completion and use of high quality research. the final combined overall system. Due to its intrinsic self-adapting Current human made application and system can be quite and self-scaling relativity properties, this system approach can be applied at any system scale: from single quantum system application fragile to unexpected perturbation because Statistics can fool development to full system governance strategic assessment policies you, unfortunately [8]. As the experiences of the 1970s, and beyond. The present paper is a relevant contribute towards a new 1980s, 1990s and 2000s have shown, unpredictable changes General Theory of Systems to show how homeostatic operating can be very disorienting at enterprise level. These major equilibria can emerge out of a self-organizing landscape of self- changes, usually discontinuities referred to as fractures in the structuring attractor points. environment rather than trends, will largely determine the

long-term future of organization. They need to be handled, as Keywords—CICT, ontological uncertainty, self-organizing opportunities, as positively as possible. system, wellbeing. Certainly, statistical and probabilistic theory, applied to all branches of human knowledge under the "continuum I. INTRODUCTION hypotesis" assumption, have reached highly sophistication LASSICAL experimental observation process, even in level, and a worldwide audience. It is the core of classic C highly ideal operative controlled condition, like the one scientific knowledge; it is the traditional instrument of risk- achieved in current, most sophisticated and advanced taking. Many "Science 1.0" researchers and scientists up to experimental laboratories like CERN [1], can capture just a scientific journals assume it is the ultimate language of small fraction only of overall ideally available information science. The basic framework of statistics has been virtually unchanged since Fisher, Neyman and Pearson introduced it. Later, the application of geometry to statistical theory and Rodolfo A. Fiorini is with the Department of Electronics, Information and Bioengineering (DEIB), Politecnico di Milano University, Milano, 32 Piazza practice has produced a number of different approaches. As an Leonardo da Vinci, MI 20133, ITALY (phone: +39 022399 3350; fax: +39 example, in 1945, by considering the space of probability 022399 3360; e-mail: [email protected]). distributions, Indian-born mathematician and statistician

ISSN: 1998-4510 29 INTERNATIONAL JOURNAL OF BIOLOGY AND BIOMEDICAL ENGINEERING Volume 9, 2015

Calyampudi Radhakrishna Rao (1920-) suggested the three kinds of uncertainty: truth uncertainty, semantic differential geometric approach to statistical inference. It uncertainty, and ontological uncertainty, the latter of which is largely focuses on typically multivariate, invariant and higher- particularly important for innovation processes and scientific order asymptotic results in full and curved exponential families research. In truth uncertainty, actors are uncertain about through the use of differential geometry and tensor analysis. whether well-defined propositions are true or not. Truth Also included in this approach are consideration of curvature, uncertainty is the only kind of uncertainty that Savage’s dimension reduction and information loss. In this way the so decision theory admits [11], where the propositions in question called "Information Geometry" (IG) approach is born. So, are statements about future consequences. Savage’s decision modern IG emerged from the study of the geometrical theory [11] claims that the truth uncertainty for all such propositions can be measured in the probability scale. Others structure of a manifold of probability distributions under the maintain Knight’s distinction between risk and uncertainty criterion of invariance. [12]: propositions about risk are probabilizable by reference to Every approach that uses analytical function applies a top- a series of fungible propositions with known truth-values: down (TD) point-of-view (POV) implicitly. These functions while others, "truly" uncertain, refer to events that have no belong to the domain of Infinitesimal Calculus (IC). such reference set and hence, according to Knight their truth Unfortunately, from a computational pespective, all uncertainty cannot be measured probabilistically. For De approaches that use a TD POV allow for starting from an exact Finetti [13], the distinction is different: propositions whose global solution panorama of analytic solution families, which truth conditions are observable are probabilizable, otherwise offers a shallow local solution computational precision to real they are not. While controversy still smolders about just what specific needs (in other words, from global to local POV the proper domain of probability is, it is certainly restricted to overall system information is not conserved, as misplaced truth uncertainty: the other two kinds of uncertainty are not precision leads to information dissipation [8]). In fact, usually probabilizable. In semantic uncertainty, actors are uncertain further analysis and validation (by probabilistic and stochastic about what a proposition means. Generating new meanings, methods) is necessary to get localized computational solution particularly new attributions of functionality for artifacts and of any practical value, in real application. A local discrete new attributions of identity for agents, is an important part of solution is worked out and computationally approximated as innovation and scientific research. the last step in their line of reasoning, that started from an The definition of ontological uncertainty depends upon the overall continuous system approach (from continuum to concept of actors’ interactions. Sometimes the entity structure discrete ≡ TD POV). Unfortunately, the IC methods are NOT of actors’ worlds change so rapidly that the actors cannot generate stable ontological categories valid for the time applicable to discrete variable. To deal with discrete variables, periods in which the actions they are about to undertake will we need the Finite Differences Calculus (FDC). FDC deals continue to generate effects. In such cases, we say that the especially with discrete functions, but it may be applied to actors face "ontological uncertainty." A quick search on continuous function too. As a matter of fact, it can deal with Google about what "made the world faster" returns as first both discrete and continuous categories conveniently. In other results: the cloud, internet, globalization, technology, wireless words, if we want to achieve an overall system information communication (and the end of the Cold War). We have begun conservation approach, we have to look for a convenient to design technologies that can take advantage of this increase bottom-up (BU) POV (from discrete to continuum view ≡ BU in the speed of information transmission to develop better POV) to start from first, and NOT the other way around! Then, short-term insights. Some claim we can now forecast the a TD POV can be applied, if needed. spreading of flu pandemics or the volatility of stocks using Deep epistemic limitations reside in some parts of the areas search query data, the results of elections using prediction covered in risk analysis and decision making applied to real markets, the demand of new products by tracking their problems [8]. As a matter of fact, to grasp a more reliable adoption by influential characters in social networks, and representation of reality, researchers and scientists need two better manage prevention of and recovery from extreme intelligently articulated hands: both stochastic and events. The availability and rapid analysis of large quantities combinatorial approach synergically articulated by natural of big data seems to often be understood as making societies coupling [9]; let’s say we need a fresh "Science 2.0" approach. "better." However, global complex socio-economic-ecological We just have to remember the Relativity’s father inspiration systems, formed by a large number of parts at different scales quote: "We cannot solve our problems with the same thinking of more or less hierarchical systems, produce emergent we used when we created them." The current paper can give a patterns and unintended consequences at various scales. A key feature of such complex interactions is that outcomes are relevant contribute to that perspective to achieve practical inherently uncertain and big data cannot reduce this operative results quite quickly. An example is presented and uncertainty. This is particularly so if the interactions are not discussed. just physical, chemical and informational but human, and hence subject to human feeling and reflexive agency. II. ONTOLOGICAL UNCERTAINTY Ontological uncertainty, in contrast to truth or semantic In 2005, Lane and Maxfield explored the relationship uncertainty, resists the formation of propositions about between uncertainty and innovation [10]. They distinguish relevant future consequences. The entities and relations of

ISSN: 1998-4510 30 INTERNATIONAL JOURNAL OF BIOLOGY AND BIOMEDICAL ENGINEERING Volume 9, 2015 which such propositions would have to be composed are Intrinsic randomness of a phenomenon (e.g. throwing a dice) "simply not known" at the time the propositions would have to or natural uncertainty cannot be reduced by the collection of be formulated, that is, during the extended present in which additional data and it stems from variability of the underlying action happens. stochastic process. On the other end, epistemic uncertainty In the fast-changing emerging scenario of continuous results from incomplete knowledge (or lack of information) technological innovation and research discoveries, ontological about the process under study. Unlike natural uncertainty, uncertainty hovers around an unaware actor. Sometimes, epistemic uncertainty can be reduced by the collection of though, system actors are completely conscious that they are additional data. immersed in ontological uncertainty, which offers no particular Statistical and applied probabilistic theory is the core of help in dealing with it. Lane and Maxfield coined the term traditional scientific knowledge; it is the "logic of science"; it ontological uncertainty [10] to refer to situations where human is the traditional instrument of risk-taking. Main epistemic agents must make decisions in a context where not only the uncertainty sources can be referred to three core conceptual future trajectory of an entity is uncertain but also its future areas: a) Entropy Generation (Clausius-Boltzmann), b) interactions with other entities and those with each other. It Heisenberg Uncertainty Principle and c) Gödel Incompleteness can also be called "radical uncertainty" and is the type Theorems. Epistemic uncertainty sources are still treated with recognised by Keynes in his well-known remarks in the the traditional approach of risk analysis, which provides an General Theory [14]. acceptable cost/benefit ratio to producer/manufacturer, but in some cases it may not represent an optimal solution to end III. A FRESH APPROACH user. In fact, deep epistemic limitations reside in some parts of The human world is moving from the Information Age to the areas covered in decision making [8]. These limitations are the Conceptual Age [15], an age that requires both creative twofold: philosophical (mathematical) and empirical (human and logical-analytical thinking, and for much of the current known epistemic biases). The philosophical problem is about theoretical work being pursued in the emerging field of the decrease in knowledge when it comes to rare events as neuroscience, computational neuroscience, and biomedical these are not visible in past samples and therefore require a cybernetics. Mankind’s best conceivable worldview is at most strong a priori, or an extrapolating theory; accordingly a partial picture of the real world, a picture, a representation predictions of events depend more and more on theories when centered on man. We inevitably see the universe from a human their probability is small. point of view and communicate in terms shaped by the exigencies of human life. However multifarious its make-up, there is a general agreement about the character of the world and the way it is ordered. Explanations of particular phenomena differ from one person to another, but without basic concurrence as to be the nature of things, there would be neither science nor common sense, agreement nor argument. The most fundamental attributes of our shared view of the world are confined, moreover, to sane, hale, sentient adults. To see the world more or less as others see it, one must above all grow up and to be quite healthy, in a wellness state, even better in a wellbeing state. The very young, like the very ill, are unable to discern adequately what is themselves and what is not. Because we cherish the past as a collective guide to behavior, the general consensus alters very slowly. Scientists as well as laymen do ignore evidence incompatible with their preconceptions. New theories which fail to fit established views are resisted, in the hope that they will prove false or irrelevant; old ones yield to convenience rather than to evidence. The 17th century Galileo Galilei's debates remind us that if you have an unshakable belief in something, then no Fig. 1. The four quadrants. The South-East area (in orange) is amount of evidence (or lack of evidence) can convince you where Statistics and models fail us.[20] otherwise (there are always anti-rationalist objections to everything and anything. It is curious, however, still to hear them in the 21st century rather than in the 17th.) In the fourth quadrant of Taleb (Fig. 1, orange square), We need tools able to manage ontological uncertainty quite knowledge is both uncertain and consequences are large, effectively [16,17]. Although there are many sources of requiring more system robustness [18]. In fact, can we uncertainty, they can be related to two basic areas of understand health without considering wild diseases and uncertainty that are fundamentally different from each other epidemics? Indeed the normal is often irrelevant. Almost and recognized as traditional reference knowledge from everything in social life is produced by rare but consequential scientific community: natural and epistemic uncertainty. shocks and jumps. All the while almost everything studied

ISSN: 1998-4510 31 INTERNATIONAL JOURNAL OF BIOLOGY AND BIOMEDICAL ENGINEERING Volume 9, 2015 about social life focuses on the "normal," particularly with humans, according to LeDoux [23]. Information about external "bell curve" methods of inference that tell you close to nothing stimuli reaches the amygdala by way of direct pathways from about natural events. Why? Because the bell curve ignores the thalamus (the "low road") as well as by way of pathways large deviations, cannot handle them, yet makes us confident from the thalamus to the cortex to the amygdala (the "high that we have tamed uncertainty. road"). The direct thalamo-amygadala is a shorter and thus a More generally, decision theory, based on a "fixed universe" faster transmission route than the pathway from the thalamus or a model of possible outcomes, ignores and minimizes the through the cortex to the amygdala. However, because the effect of events that are "outside model". A fixed model direct pathway bypasses the cortex, it is unable to benefit from considers the "known unknowns", but ignores the "unknown cortical processing. As a result, it can only provide the unknowns" [19,20]. It is not a word pun and if we can use an amygdala with a crude representation of the stimulus. It is thus analogy, it is like to talk about the difference between "secrets" a quick and dirty processing pathway. The direct pathway and "mysteries." Secrets being things that were knowable but allows us to begin to respond to potentially dangerous stimuli we just don’t know them, and mysteries being things that are before we fully know what the stimulus is. This can be very basically unknowable, as the difficulty that policy-makers have useful in dangerous situations. However, its utility requires in making decisions about things because of the information that the cortical pathway be able to override the direct they don’t have, the imponderables. The idea of known and pathway. It is possible that the direct pathway is responsible unknown unknowns recognizes that the information those in for the control of emotional responses that we do not positions of responsibility in government, as well as in other understand. The time saved by the amygdala in acting on the human endeavors, have at their disposal is almost always thalamic information, rather than waiting for the cortical input, incomplete. It emphasizes the importance of intellectual may be the difference between life and death. It is better to humility, a valuable attribute in decision making and in have treated a stick as a snake than not to have responded to a formulating strategy. possible snake. It is difficult to accept, to know that there may be important Most of what we know about these pathways has actually unknowns. The best strategists try to imagine and consider the been learned by studies of the auditory as opposed to the possible, even if it seems unlikely. They are then more likely visual system, but the same organizational principles seem to to be prepared and agile enough to adjust course if and when apply. The low road is a pathway which is able to transmit a new and surprising information requires it, when things that signal from a stimulus to the thalamus, and then to the were previously unknown become known [20]. So, we have amygdala, which then activates a fear-response in the body. even to think about uncertainty in the characterisation of This sequence works without a conscious experience of what uncertainty by counterfactual thinking. Counterfactual thinking comprises the stimulus, and it is the fast way to a bodily is a concept in psychology that involves the human tendency to response (a more primitive mechanism of defense). The high create possible alternatives to life events that have already road is activated simultaneously. This is a slower road which occurred; something that is contrary to what actually also includes the cortical parts of the brain, thus creating a happened. Counterfactual thinking is exactly as it states: conscious impression of what the stimulus is (a more "counter to the facts" [21]. These thoughts consist of the sophisticated mechanism of defense). "Amygdala hijack" is a "What if?" and the "If I had only..." that occur when thinking term coined by psychologist D. Goleman [25]. Drawing on the of how things could have turned out differently. Counterfactual work of Joseph E. LeDoux, Goleman uses the term to describe thoughts are things that could never possibly happen in reality, emotional responses from people which are immediate and because they solely pertain to events that have occurred in the overwhelming, and out of measure with the actual stimulus past [21]. because it has triggered a much more significant emotional While the advantage of differentiating between natural threat. From the thalamus, a part of the stimulus goes directly (aleatoric) and epistemic uncertainty in analysis is clear, the to the amygdala (low road) while another part is sent (high necessity of distinguishing between them is not, by an road) to the neocortex (the "thinking brain"). If the amygdala operative point of view. As a matter of fact, epistemic and perceives a match to the stimulus, i.e., if the record of aleatory uncertainties are fixed neither in space nor in time. experiences in the hippocampus tells the amygdala that it is a What is aleatory uncertainty in one model can be epistemic fight, flight or freeze situation, then the Amygdala triggers the uncertainty in another model, at least in part. And what HPA (Hypothalmic-Pituitary-Adrenal) axis and hijacks the appears to be aleatory uncertainty at the present time may be rational brain. This emotional brain activity processes cast, at least in part, into epistemic uncertainty at a later date information milliseconds earlier than the rational brain, so in [22]. case of a match, the amygdala acts before any possible To get deeper inspiration, we focus our attention on direction from the neo-cortex can be received. If, however, the mammalian brain neurophysiology. In fact, from a amygdala does not find any match to the stimulus received neurophysiological point of view, neuroscientist Joseph E. with its recorded threatening situations, then it acts according LeDoux finds two amygdala pathways in the brain of the to the directions received from the neo-cortex. When the laboratory mouse by the use of fear conditioning and lesion amygdala perceives a threat, it can lead that person to react study [23,24]. Although most of the research on the neural irrationally and destructively. basis of conditioned fear has been conducted on animals, fear Taking into consideration the neurophysiological findings conditioning procedures can be used in identical ways in by LeDoux, differently from the past, it is much better to

ISSN: 1998-4510 32 INTERNATIONAL JOURNAL OF BIOLOGY AND BIOMEDICAL ENGINEERING Volume 9, 2015 consider ontological uncertainty [23] as an emergent Intelligence (EI) and Emotional Creativity (EC) [25] coexist at phenomenon out of a complex system. Then, our dynamic the same time with Rational Thinking in human mind, sharing ontological perspective can be thought as an emergent, natural the same input environment information [26]. Therefore, the operating point out of, at least, a dichotomy of two mathematical method we are looking for, must possess even fundamental coupled irreducible complementary ideal anticipatory properties, at design level, needed to the asymptotic concepts: a) reliable predictability and b) reliable realization of system capable to interact with its environment unpredictability. in real time (leading property) [27]. From TD management perspective, the reliable predictability concept can be referred to traditional system IV. CICT reactive approach (lag subsystem, Closed Logic, to learn and The first attempt to identify basic principles, to synergically prosper) and operative management techniques. The reliable articulate Computational Information Conservation Theory unpredictability concept can be associated to system proactive (CICT) by natural coupling to IG, for scientific research and approach (lead subsystem, Open Logic, to survive and grow) application, has been developing at "Politecnico di Milano and strategic management techniques. University" since the end of last century. In 2013, the basic To achieve our final goal, overall system must be provided principles on CICT, from discrete system parameter and with smart sensing interface which allow reliable real-time generator, appeared in literature and a brief introduction to interaction with its environment. To behave realistically, CICT was given in 2014 [9]. CICT tries to bring classical and system must guarantee both Logical Aperture (to survive and quantum information theory together in a single formalism, by grow) and Logical Closure (to learn and prosper), both fed by considering information not only on the statistical manifold of environmental "noise" (better… from what human beings call model states but also from empirical measures of low-level "noise") [2]. multiplicative noise source generators, related to experimental high-level overall perturbation [2]. CICT showed that long arithmetic division minority components (Remainders, R), for long time concealed relational knowledge to their dominant result (Quotient, Q), not only can always allow quotient regeneration from their remainder information to any arbitrary precision, but even to achieve information conservation and entropy minimization, in systems modeling and post-human cybernetic approaches [28,29]. Number Theory and modern Numeric Analysis use mono- directional interpretation (left-to-right, LTR) only, for Q Arithmetic single numeric group generator, so information entropy generation cannot be avoided in current computational algorithm and application [30]. As a matter of fact, traditional digital computational resources are unable to capture and to manage not only the full information content of a single Real Number R, but even Rational Number Q information content is managed by information dissipation. On the contrary, according to CICT, it is quite simple to show information conservation and generator reversibility (right-to-left, RTL), by using basic considerations only. Traditional elementary arithmetic long division remainder sequences can be interpreted as combinatorially optimized exponential cyclic sequences (OECS) for hyperbolic geometric structures, as points on a discrete Riemannian manifold, under HG metric, indistinguishable from traditional random noise Fig. 2 Operating Point can emerge as a new Trans-disciplinary sources by classical Shannon entropy, and contemporary most Reality Level (TRL), based on Two Complementary advanced instrumentation [2]. Thanks to this brand new Irreducible Management Subsystems interacting with their knowledge and following this line of generative thinking, it is common environment [26]. possible immediately to realize that traditional Q Arithmetic can be even interpreted, by new eyes, as a highly sophisticated open logic, powerful and flexible LTR and RTL evolutionary, So, according to previous considerations, at brain level, it is generative, formal numeric language of languages, with self- possible to refer to LeDoux circuit ("low road", Logical defining consistent numeric words and rules, starting from Aperture) for emotional behavior (i.e. fear, emotional elementary generator and relation (you get your specific intelligence, etc.) and to Papez circuit ("high road", Logical formal numeric language by just simply choosing your most Closure) for structured behavior (i.e rational thinking, convenient numeric base to polynomially structure your knowledge extraction, etc…) as from Fig.2 [23,24]. Emotional information). By this new perspective, traditional rational

ISSN: 1998-4510 33 INTERNATIONAL JOURNAL OF BIOLOGY AND BIOMEDICAL ENGINEERING Volume 9, 2015 representations are able to capture two different type of contains itself. Traditionally, such statements lead to paradox, information at the same time, both modulus (usual quotient a form of inconsistency. In the informal fallacies self- information) and associated intrinsic period information which referential statements are considered poor form. That is true in each combined generator inner phase can be computed from. mathematics and arithmetics when you use a continuum So, rational information can be better thought to be isomorphic support approach and do not take advantage from the scale to vector information at least, rather than to usual scalar one relativity finiteness limitations of your real computational only. resources as CICT does [2,9]. The final result is CICT new awareness of a hyperbolic framework of coded heterogeneous hyperbolic structures, V. RESULTS underlying the familiar Euclidean surface representation In his book "Liber abaci", for the first time Fibonacci system. CICT emerged from the study of the geometrical (1170-1250) introduced the concept of recursive sequence to structure of a discrete manifold of ordered hyperbolic the Western culture, with the famous sequence: substructures, coded by formal power series, under the criterion of evolutive structural invariance at arbitrary 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.89, 144, ... (01) precision. It defines an arbitrary-scaling discrete Riemannian manifold uniquely, under HG metric, that, for arbitrary finite in which each term is the sum of the two preceding ones and point accuracy level L going to infinity (exact solution the numerical sequence composition law can be written: theoretically), is isomorphic, even better homeomorphic, to traditional IG Riemannian manifold. In other words, HG can Fn = Fn-1 + Fn-2 with F0 = 0 and F1 = 1 , (02) describe a projective relativistic geometry directly hardwired into elementary arithmetic long division remainder sequences, and in general, Fn = k1* Fn-1 + k2* Fn-2 , where k1, k2 = offering many competitive computational advantages over 0,1,2,…∞, k , k  N, for Generalized Fibonacci Sequences. traditional Euclidean approach [2]. 1 2 For original Fibonacci sequence k1= k2 = 1. In the past five decades, trend in Systems Theory, in As a starting point, this relation can be thought as the specialized research area, has shifted from classic single aggregation of an external information [F , F ]≡[u , u ] to domain information channel transfer function approach 0 1 1 2 internal system status information [k1, k2]. Therefore, recursive (Shannon's noisy channel) to the more structured ODR sequence information aggregation offers at least three Functional Sub-domain Transfer Function Approach operational advantages over usual direct polynomial (Observation, Description and Representa-tion), according to quantification. First, recursive sequence information CICT Infocentric Worldview model (theoretically, virtually aggregation does not suffer from the computational polynomial noise-free data) [2]. mirroring effect. Second, its asymptotic convergence CICT sees rational geometric series as simple recursion properties computed by the ratio of successive terms allows sequences in a wider recursive operative framework where all the creation of a structured system's behavioral space similar, algebraic recursion sequences of any countable higher order in computational behavior, to the living organism's include all the lower order ones and they can be optimally homeostasis (i.e. the automatic selection of environment's mapped to rational number system Q operational minimum perturbation level that allows optimal interaction representations and generating functions. For instance, between external information from environment (u) and arithmetic progression and Lucas sequences are recursion system internal status information (k) [31], as evidenced by sequences of the second order. Lucas sequences are certain Holling [26]. Third, recursive sequence information integer sequences that satisfy Lucas recurrence relation aggregation represents a computational method with intrinsic defined by polynomials Un(P,Q) and Vn(P,Q), where Un, Vn computational anticipatory properties, because it is possible to are specific polynomials and P, Q are fixed integer structure anticipatory computation for successive sequence coefficients. Any other sequence satisfying this recurrence terms arbitrarily. Then taking any positional index it is relation can be represented as a linear combination of the possible to compute not only the next one but also those ones Lucas sequences Un(P,Q) and Vn(P,Q). Famous examples of at any distance from the current position in an anticipatory way Lucas sequences include the Fibonacci numbers, Mersenne [27]. Moreover, the ratio of Fibonacci sequence's two numbers, Pell numbers, Lucas numbers, Jacobsthal numbers, consecutive numbers, according to the relation: and a superset of Fermat numbers. CICT is able to fold any recursion sequence of the first order into one digit number D1, F n1 any recursion sequence of second order into a two digit lim    number D2, any recursion sequence of the third order into a n  (03) F n  three digit number D3 and so on to higher orders. Then, you can interpret their asymptotic convergence ratios as increasing accuracy approximations to related asymptotic roots from asymptotically converges to the golden number, property corresponding first, second, third, ..., n-th order equations discovered by Kepler [32], providing us with recurrence respectively. relation functional closure. We already know about "self-reference" in mathematics as a For this simplest case, the recursive aggregation law of statement that refers to itself, for example, as a set that information can be easily extended to three consecutive terms (starting by trinomial 0,0,1, third order relation, m=3), four

ISSN: 1998-4510 34 INTERNATIONAL JOURNAL OF BIOLOGY AND BIOMEDICAL ENGINEERING Volume 9, 2015 successive terms (starting by quadrinomial 0,0,0,1, fourth conservation by irreducible complementary system) [2]. But, order relation , m=4), j successive terms (starting by m-nomial never forget one of Robert Rosen’s fundamental lessons: formed by j zeroes, plus one 1, (j+1)th order relation, (m=j+1), human formal systems are unable to capture enough and in general we can write, in compact form, recursive knowledge to model natural system completely [27]. You have relations as function of three parameters, an = a(m, k, u), as to model natural system with deep awareness to grasp a part of specified previously, where m is the recurrence relation order. it only! What you will always get is uncertainty awareness evolutive finite scale relativity precision from never-ending natural evolution. So the best you can do is to find your best strategic management solution to handle arbitrary incomplete knowledge and system uncertainty precision [2,9]. Rational recursive sequence represents a convenient mathematical method that holds anticipatory proprieties, because it is possible to implement the anticipatory computation of any recursive sequence’s term. Taking arbitrarily any current positional index, it is possible to describe not only the next term but also terms at a certain distance from the current one in an anticipatory way, compared with the current positional index, by implementing its primary relation recursion conveniently. Specifically, starting from the recursive rule that indicates the next term to the current one, it Fig. 3 Control Value k allows to arrange external inputs u into is possible to structure a set of rules that allows to obtain symbolic string information with different convergence rate recursive sequence’s terms at different distance, defining a set approximation around their convergence rate asymptotic value of registers that, working in parallel, are able to provide values (World Cloud). For different k values, a landscape of world with the desired anticipation level immediately. For example, clouds can start self-organizing into a Baire Space. Control considering second order (m = 2) recursive relations an = a(2, Value k selects recurrence series asymptotic convergence rate k, u), where k and u are 2-d vectors [k1, k2] and [u1, u2] (Attractor Point), which different input u approximated rates respectively, and where the (n + 1)-th to the current n-th term are self-arranging modularly (World Cloud) around. is obtained in the following way:

an+1 = k1 * an + k2 * an-1 , (04) In this way, we can allow for articulated information aggregation even in a networking environment and computing where an-1 = u1 = 0 and an = u2 = 1, k1= k2 = 1, for the their related asimptotic functional closures immediately. Fibonacci sequence. Then, we can specify recursion derived Therefore, it is possible to compute recursively further relations to compute appropriate terms at any arbitrary numerical sequences asymptotically converging to irrational distance from the current position n. As an example, we define limits or completely diverging as function of external the following relations that are valid for computing terms to information input. In this way system can search automatically the distance n+5 from the current one, depending, for instance, for a minimum environmental perturbation level (system on parameters [k1, k2] = [1, 1] and [k1, k2] = [2, 2]. These internal status) useful to insure sequence asymptotically recursive relations can be used in parallel, respectively, to convergence to get vital information from system environment provide the terms of sequence in an anticipatory way (self-regulation and learning as quest for the difference that simultaneously. So in the case of [k1, k2] = [1, 1], aggregation makes the difference, probing by probing...). Then, rules are as follows: homeostatic operating equilibria can emerge out of a self- organizing landscape of self-structuring attractor points with an+2 = 2 * an + 1* an-1 their World Cloud (Fig.3). an+3 = 3 * an + 2 * an-1 (05) Irrational numeric limit families, identified by converging an+4 = 5 * an + 3 * an-1 recursive numeric sequences allow the structuring of a an+5 = 8 * an + 5 * an-1 mathematical Baire’s Space. A Baire space consists of … . countably infinite sequences with a metric defined in terms of the longest common prefix: the longer the common prefix, the In the case of values [k1, k2] = [2, 2] we obtain the following closer a pair of sequences. What is of interest to us here is this aggregation rules: longest common prefix metric, which we call the "Baire distance", which is an ultrametric distance [33,34,35]. Baire’s an+2 = 6 * an + 4 * an-1 Space allows to manage numeric information in a way useful an+3 = 16 * an + 12* an-1 (06) to synthetise quick and raw system primary response "to an+4 = 44 * an + 32 * an-1 survive and grow." Furthermore, in this way system can even an+5 = 120 * an + 88 *an-1 automatically self-organize and structure numeric families with ... . different numerical closure to conserve overall system information (Generalized Fibonacci Systems, and information

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In general for any vector [k1, k2] and for any order m, it is adaptive and learning system reference architecture for always possible to formulate rules associated to their primary anticipatory smart system interface (Interaction Interface recursion relation: these rules allow for the parallel System, IIS) is depicted in Fig.5. The simple recursive anticipatory computation of recursive sequence’s term at any information aggregation method can be used even for distance from the current term position n. advanced ISS (Inner Safety System) in advanced biomedical To synthetize more organized and articulated, but slower, and healthcare system development, for neuroperception, system response "to learn and prosper", it is necessary to organ level modeling, bio-transduction functions, etc. structure recursive information into an "ordered polynomial reference", by "polynomial weighing" mapping, to obtain "coherent perception" [31]. Polynomial weighing is key numeric operation to map recursive sequence information representation into polynomial format corresponding to combinatorially OECS, folded into rational number operative representation (Fig.4) [2,9].

Fig. 5 Interaction Interface System (IIS) Reference Architecture [31]: Apprehension (Open Logic Section); Organization (Closed Logic Section).

Due to its intrinsic self-organizing and self-scaling properties, this system approach can be applied at any system scale: from single health application development to full healthcare system governance strategic simulation and assessment application [28]. It can allow both quick and raw system response (Open Logic response, to grow and survive) and slow and accurate information unfolding for future response strategic organization (Closed Logic response, to learn, to adapt and prosper) by coherently formatted operating point [28].

VI. AN APPLICATION EXAMPLE To design, analyse and test IIS and ISS system properties, a simulation environment has been designed, developed and implemented, programmed in MATLAB language, called VEDA® (Visualization of Evolutionary Dynamics Application), at Politecnico di Milano University. VEDA® system dynamics simulation toolbox offers a high level simulation flexibility by user-optimized graphic interface to get easier simulation task, to design, analyze and synthetize Fig. 4 Polynomial Weighing mapping allows the modular complex dynamical system behaviour. In this way, it is mapping of each 2-D approximated algebraic irrational World possible to study natural complex dynamic’s simulation, to Cloud into a corresponding Rational Word Family. verify and validate through numerical computation and Denominator D identifies Rational Word Family. Numerator N displaying the behavior of all subsystems that compose the identifies algebraic rational approximations of irrational values final combined overall system performance. So, according to (attractor points) as component inside that Family. desired system parameters, to validate the choice of optimal

parameters set, for a specific embodiment, is quite

straightforward [31]. So, we get a sequence of different structuring operations to Here, as an application example, we use VEDA for data get external information more and more coherently formatted processing and pattern recognition in a cognitive task to system internal status to arrive to a system "coherent application (spoken sentence comprehension) using perception" of external information. In this way, a natural electroencephalography (EEG) data [36] and event related balanced "Operating Point" can emerge, as a new Trans- potentials (ERP) preprocessing [37]. disciplinary Reality Level, from an irreducible complementary Brain ultimately depends on the knowledge of large-scale ideal asymptotic dichotomy: Two Coupled Complementary networks organization (i.e. Default mode net, Salience net, Irreducible Information Management Subsystems. The overall Central-executive net, Mirroring net, Mentalizing net, etc.)

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[38]. The Default Mode Network (DMN) regions exhibit most common of these procedures involves averaging samples deactivation during a wide variety of resource demanding of the EEG that are time-locked to repeated occurrences of a tasks. However, recent brain imaging studies reported that they particular event or type of event. The number of samples used also show activation during various cognitive activities. In in the average is related to the signal-to-noise ratio [41]. addition, studies have found a negative correlation between the However, in all cases, the samples are selected so that they DMN and the Working Memory Network (WMN). Activation bear a consistent temporal relationship to the event. Because of these network regions is affected by allocation of attentional aspects of the EEG that are not time-locked to the event are resources to the task relevant regions due to task demands. The assumed to vary randomly from sample to sample, the core DMN regions exhibit activation during task preparation averaging procedure should result in a reduction of these noise and deactivation during task execution [38]. Human brain potentials, rendering the signal, event-related potentials visible contains broadly distributed functional networks that can each [37]. Because ERPs are always measured as differences in be redescribed as basic psychological operations that interact potential between two recording locations, they will also vary to produce a range of mental states, including, but not limited as a function of the electrode site at which they are recorded, to, anger, sadness, fear, disgust, and so on. When compared to as well as the reference electrode used. Spatial (topographic) the faculty psychology approach, this approach provides an distribution is regarded as an important discriminative alternative functional architecture to guide the design and characteristic of the ERP [42]. Therefore, positive and interpretation of experiments in cognitive neuroscience. negative peaks in the ERP are generally described in terms of Continued progress in understanding of cognitive function their characteristic scalp distribution, as well as their polarity, and dysfunction will depend on the development of new and latency. techniques for imaging structural and functional brain connectivity, as well as on new computational tools and methods for investigating deep dynamic interactions within and between brain networks. For instance, spoken sentence comprehension relies on rapid and effortless temporal integration of speech units displayed at different rates. Temporal integration refers to how chunks of information perceived at different time scales are linked together by the listener in mapping speech sounds onto meaning. The neural implementation of this integration remains unclear [40]. The role of short and long windows of integration in accessing meaning from long samples of speech plays a fundamental role. In a cross-linguistic study, the time course of oscillatory brain activity between 1 and 100 Hz, was recorded using EEG, during the processing of native and foreign languages. Oscillatory responses in a group of Italian and Spanish native speakers while they attentively listen to Italian, Japanese, and Spanish utterances, played either forward or backward, was recorded. The results show that both groups of participants display a significant increase in gamma band power (55-75 Hz) only when they listen to their native language played forward. The increase in gamma power starts around 1000 msec after the onset of the utterance and decreases by its end, resembling the time course of access to meaning during speech perception [40]. In contrast, changes in low-frequency power show similar patterns for both native and Fig. 6 A typical ERP preprocessing from EEG data recording foreign languages. So, it seems that gamma band power for our example where you can see a few standard reference reflects a temporal binding phenomenon concerning the points: Main Stimulus starting at t = 0, tp onset ending, P1 coordination of neural assemblies involved in accessing Sensory Gating, Ne Error Detection, N1 Trend Response, P2 meaning of long samples of speech [40]. The final goal is to Cortical Gate Tune, N2 Recognition and Selection, N3 New try to reach a better understanding of how the human brain Meaningful Stimuli Attention Shift (see text). produces cognition. Continuous EEG data were acquired using a 64-channel electrode cap with standard 10-10-system electrode placement Let’s assume that a standard ERP for our example is [36]. A typical ERP preprocessing is applied to EEG data reportend in Fig.6 where you can see a few standard temporal recording [37]. The ERP is small (a few microvolts) in reference points: Main Stimulus starting at t = 0, tp onset comparison to the EEG (about 50 microvolts). Thus, analysis ending, P1 Sensory Gating, Ne Error Detection, N1 Trend generally begins with procedures to increase the discrimination Response, P2 Cortical Gate Tune, N2 Recognition and of the signal (the ERP) from the noise (background EEG). The Selection, N3 New Meaningful Stimuli Attention Shift, etc.

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The N1 is such an example, as it is assumed to be sensitive to both the physical properties of the stimulus and the nature of the interaction between the subject and the event (e.g., whether the event is to be attended) [37]. On the right side of Fig.7 a VEDA fitting, computational model of the P1 onset response is synthezised by a fifth order LTR recurrence relation (please, note that the function is flipped according to recording polarity). Now, according to CICT, it is possible to get a unique RTL function extension by information conservation, as reported on the left side of Fig.8, giving a divergent oscillating function, apparently difficult to offer any immediate interpetation. Nevertheless, applying the information coherent combinatorial approach allowed by CICT, VEDA toolbox displays our final result in the left side of Fig.9. As a matter of

Fig. 7 Enlargement of the ERP onset inside the black circle of fact, the previous divergent oscillating function is the coherent Fig.6. Right side: CICT fitting of the function on the left side combination of five combinatorially optimized subsequences. from t = 0 to instant tp, by a divergent LTR recursive sequence So, even the previously assumed simple interpretation of the (see text). onset response from t = 0 to tp should be more carefully revisited. In fact, according to VEDA interpretation, it could be the overall response result due to the coherent composition Usually, the recording temporal behavior interpretation is of five different subsytem outputs, which start to cooperate to quite easy from t = 0 to tp. In fact, the usual assumption is that one another immediately on input stimuli. only one or two components start responding to input stimuli. As farer as you go from t = 0, subsystems behavior start to show interplay couplings getting more difficult to arrive to a clear interpretation of single subsystem contribute to overall system response. The labels given to the peaks of an ERP waveform often include descriptors of polarity and latency. In Fig.7, on the left side, you can see an enlargement of the early ERP P1 onset inside the black circle of Fig.6 (from t = 0 to tp). Traditionally, although the exogenous/endogenous distinction provides a useful method for classifying many ERP components, there are potentials that possess characteristics that are intermediate between these two groups, and are therefore called "mesogenous" [42].

Fig. 9 Coherent combination of five simple RTL slave subsequences to synthesize the unique LTR master sequence on the right side (see text).

VII. CONCLUSION The major added value of our paper is provided by our fresh approach to ontological uncertainty management and by our new idea of system articulated interaction, defined by inner and outer system information aggregation. It can allow both quick and raw system response (to survive and grow) and slow and accurate information unfolding for future response strategic organization (to learn and prosper) by coherently formatted operating point [31]. Now, new advanced systemic Fig. 8 Divergent LTR recursive sequence (upper right side) information application can successfully and reliably manage a generated by apparently irregularly arranged point RTL higher system complexity than current ones, with a minimum divergent sequence on the left (see text).

ISSN: 1998-4510 38 INTERNATIONAL JOURNAL OF BIOLOGY AND BIOMEDICAL ENGINEERING Volume 9, 2015 of design constraints specification and less system final organization (Closed Logic response, to adapt and prosper) by operative environment knowledge at design level. coherently formatted operating point information. For closed For instance, according to Fig.2, at brain level, it is possible logic Reactive Management system, we can choose from to refer to LeDoux circuit (Logical Aperture) for emotional different documented operational alternatives offered by behavior (i.e. fear, emotional intelligence, etc…) and to Papez literature, like Deming’s PDCA Cycle [43], Discovery-Driven circuit (Logical Closure) for structured behavior (i.e rational Planning [44], etc…, while for open logic Proactive thinking, knowledge extraction, etc…) [23,24]. Emotional Management system, we can choose from Boyd OODA Cycle Intelligence (EI) and Emotional Creativity (EC) [25] coexist at (1987) [45], Theory-Focused Planning [46,] etc… As a simple the same time with Rational Thinking in human mind, sharing example, PDCA’s cycle (Reactive Management) and OODA’s the same input environment information [26]. Then, operating cycle (Proactive Management) can be selected to represent two point can emerge as a trans-disciplinary reality level from the corresponding complementary irreducible sub-systems for interaction of two complementary irreducible, asymptotic ideal advanced integrated strategic management. Then, our final coupled subsystems with their common environment. To operative reference architecture, for Safety and Effectiveness behave realistically, overall system must guarantee both Health Systemic Governance, is given as from Fig.10. Logical Aperture (to get EI and EC, to survive and grow) and Logical Closure (to get Rational Thinking, to learn and prosper), both fed by environmental "noise" (better… from what human beings call "noise") [2]. In fact, natural living organism does perturb its environment, but only up to the level it is perturbed in turn by its own environment both to survive and grow, no more [26]. Due to its intrinsic self-scaling relativity properties, this system approach can be applied at any system scale: from single quantum system application development to full system governance strategic assessment policies and beyond [28]. We can use the same nonlinear logic approach to guess a convenient basic architecture for Anticipatory Learning System (ALS) to get realistic modeling of natural behaviour to be used in High Reliable Organization (HRO) application development. As an example, we showed that traditional data processing and pattern recognition in a cognitive task application (spoken sentence comprehension), using electroencephalography (EEG) data and ERP preprocessing, can offer a shallow interpretation of experimental data unfortunately. A deeper interpretation can be reached by CICT approach and VEDA analysis. In this case, brainsteam function can be exploited much better for system modeling. The overall response result emerges out of the coherent composition of five different subsytem outputs, which start to cooperate to one another immediately on input stimuli onset. CICT coherent representation precision leads to more experimental information clarity and conservation. VEDA® is an original simulation environment developed to validate complex dynamical system modeling. IIS and ISS are two pivotal concepts to develop safer, more adequate, effective and efficient solutions for competitive safety systems and human wellbeing. As a matter of fact their basic operational concepts can be conveniently and successfully extended to many other advanced Business and HRO application areas, with no performance or economic penalty, to develop more and more competitive application. For instance, at a higher level of Fig. 10 Final Architecture for Safety and Effectiveness Health abstraction, environmental noise input information to be Systemic Governance. aggregated to system internal status information can provide a structured homeostatic synthetic operating point as a reference for further inquiry. Then, System Interaction by internal and Specifically, advanced wellbeing applications (AWA), high external information aggregation can allow both quick and raw reliability organization (HRO), mission critical project (MCP) response (Open Logic response, to grow and survive) and slow system, very low technological risk (VLTR) and crisis and accurate information for future response strategic management (CM) system will be highly benefited mostly by CICT newer approach and related techniques. The present

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Rodolfo A. Fiorini is tenured Professor of Bioengineering at the Department of Electronics, Information and Bioengineering (DEIB) of the Politecnico di Milano University, Italy. In 1979, Dr. Fiorini was awarded for "Energetics Fellowship" from the Italian Ministry of Scientific Research and University and attended Bocconi University, School of Economics, and Politecnico di Milano University, specializing in Energetics. He gained his Ph.D. degree in Energetics (100/100) from Politecnico di Milano University, in 1984. In the 1980s, Dr. Fiorini was research associate to Stanford University (SU), Department of Aeronautics and Astronautics, Stanford, CA, U.S.A. and to University of California at Los Angeles (UCLA), Department of Computer Science, CA, U.S.A. The U.S.A. DOL appointed him with the Ph.D. degree in Bioengineering in 1989. A senior member of the IEEE and the EMBC, member of the WSEAS, Dr. Fiorini founded the Research Group on Computational Information Conservation Theory (CICT), and he is responsible for the main course on Wellbeing Technology Assessment at DEIB. Author of more than 230 national, international, scientific and technical, articles, papers, seminars, presentations and books. His current research interests include biomedical cybernetics, neuroscience, wellbeing, consciousness, nanoscience, computer simulation techniques, information theory, anticipatory learning systems, networked-control systems, machine learning, machine intelligence, statistical and deterministic signal processing, statistical and combinatorial optimization techniques, decision support systems, advanced management systems.

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